Thermal Vacuum Radiation in Spontaneously Broken Second-Quantized Theories on Curved Phase Spaces of Constant Curvature

TL;DR

This paper explores how second-quantized theories on curved phase spaces exhibit thermal radiation due to spontaneously broken symmetries, linking curvature to quantum statistics and discussing implications for dark energy and inflation.

Contribution

It constructs second-quantized theories on coset spaces of pseudo-unitary groups and analyzes the resulting thermal radiation and symmetry breaking effects in curved phase spaces.

Findings

Positive curvature relates to generalized Fermi-Dirac statistics.

Negative curvature relates to generalized Bose-Einstein statistics.

Vacuum energy contributions may influence cosmological constant and inflation.

Abstract

We construct second-quantized (field) theories on coset spaces of pseudo-unitary groups U(p,q)$. The existence of degenerated quantum vacua (coherent states of zero modes) leads to a breakdown of the original pseudo-unitary symmetry. The action of some spontaneously broken symmetry transformations destabilize the vacuum and make it to radiate. We study the structure of this thermal radiation for curved phase spaces of constant curvature: complex projective spaces CP^{N-1}=SU(N)/U(N-1) and open complex balls CD^{N-1}=SU(1,N-1)/U(N-1). Positive curvature is related to generalized Fermi-Dirac (FD) statistics, whereas negative curvature is connected with generalized Bose-Einstein (BE) statistics, the standard cases being recovered for N=2. We also make some comments on the contribution of the vacuum (dark) energy to the cosmological constant and the phenomenon of inflation.